Transition strengths and the role of the $f_{7/2}$ orbital in ${}^{71}\mathrm{As}$

High-spin states in ${}^{71}\mathrm{As}$ were studied using the ${}^{54}\mathrm{Fe}$$({}^{23}$Na,$\alpha 2p)$ reaction at 80 MeV. Prompt $\gamma$-$\gamma$ coincidences were measured using the Florida State University Compton-suppressed Ge array consisting of three clover detectors and seven single-crystal detectors. The existing high-spin level scheme has been verified, and 21 new transitions have been added based on an investigation of weak $\gamma$-ray coincidence relations and relative $\gamma$-ray intensities. Lifetimes of 16 excited states were measured using the Doppler-shift attenuation method applied to the experimental line shapes of decays in all of the known rotational bands. The $B(E2)$ strengths inferred from the lifetimes indicate that moderate to high collective behavior persists to the highest observed spins in the lowest positive- and negative-parity bands, in qualitative agreement with projected shell-model calculations. The band suggested to be based on the $\pi f_{7/2}$ orbital shows a similar degree of collectivity within the same spin range, with $B(E2)$ values in good agreement with those predicted by the projected shell model assuming a constant prolate deformation of ${\epsilon }_2=+0.27$. The experimental $Q_t$ values in this band are somewhat smaller than predicted by cranked Woods-Saxon calculations.

Figure 1

Partial level scheme of ${}^{71}\mathrm{As}$ relevant to the present work. Transitions introduced in this work are indicated with asterisks. The energies and decay intensities of all other transitions originating from positive-parity (negative-parity) states were taken from Ref. [2] ([3]). The arbitrary labels above each decay sequence are included to facilitate the discussion in the text.

Figure 2

A portion of the background-corrected coincidence spectrum obtained by gating on the 996.0-keV transition as measured by the 90${}^{°}$ detectors. Peak energies labeled with asterisks indicate transitions assigned to ${}^{71}\mathrm{As}$ in this work.

Figure 3

Representative fits to the 35${}^{°}$ line shapes of transitions belonging to band 1 in ${}^{71}\mathrm{As}$. Spectra obtained by gating from above (GFA) or gating from below (GFB) the transition of interest are indicated. Some error bars are smaller than the symbol size.

Figure 4

Representative fits to the 35${}^{°}$ or 145${}^{°}$ line shapes of transitions between negative-parity states in ${}^{71}\mathrm{As}$. Spectra obtained by gating from above (GFA) or gating from below (GFB) the transition of interest are indicated. Some error bars are smaller than the symbol size. The contaminant in the shifted portion of the line shape of the 442.6-keV transition (bottom panel) was not included when performing the fit.

Figure 5

Kinematic ($J^{(1)}$) and dynamic ($J^{(2)}$) moments of inertia as a function of rotational frequency $\hslash \omega$ for bands 1, 3, and 4 in ${}^{71}\mathrm{As}$. A common value of $K=\frac{5}{2}$ was used for all bands.

Figure 6

$B(E2)$ strengths as a function of the initial-state spin for band 1 (top panel), bands 3 and 4 (middle), and bands 6 and 7 (bottom) in ${}^{71}\mathrm{As}$. Filled (open) circles indicate experimental values associated with a signature $\alpha =+\frac{1}{2}$ ($-\frac{1}{2}$) sequence. Symbols with arrows indicate either upper or lower limits established by the lifetime measurements, and one experimental value (corresponding to an initial state of ${\frac{25}{2}}^{+}$ in band 1) has error bars that are smaller than the symbol size. The solid curves represent theoretical predictions from projected shell-model calculations.

Figure 7

$B(M1)$ strengths as a function of the initial-state spin for the $M1$ transitions between bands 6 and 7 in ${}^{71}\mathrm{As}$. Filled (open) circles indicate experimental values associated with a signature $\alpha =+\frac{1}{2}$ ($-\frac{1}{2}$) sequence. Symbols with arrows indicate either upper or lower limits established by the lifetime measurements. The solid curve represents theoretical predictions from projected shell-model calculations.

Figure 8

Energy differences between adjacent spin states in bands 6 and 7 in ${}^{71}\mathrm{As}$, determined experimentally (circles) and theoretically using projected shell-model calculations assuming a prolate deformation of ${\epsilon }_2=+0.27$ (triangles), and oblate deformations of ${\epsilon }_2=-0.2$ (squares) and $-0.3$ (diamonds). Filled (open) symbols indicate states with spin $I$ associated with a signature $\alpha =+\frac{1}{2}$ ($-\frac{1}{2}$) sequence. The experimental results assume a ${\frac{7}{2}}^{-}$ band head at an excitation energy of 1729.0 keV.

Figure 9

Sample total Routhian surfaces in the $({\beta }_2,\gamma )$ plane for an intrinsic quasiparticle configuration that most likely represents band 7 in ${}^{71}\mathrm{As}$ at rotational frequencies of $\hslash \omega =0.3$ (top) and 0.5 MeV (bottom). The spacing between contour lines is 200 keV.

Figure 10

Transition quadrupole moments $\left|Q_t\right|$ as a function of rotational frequency for bands 6 and 7 in ${}^{71}\mathrm{As}$. Filled (open) circles indicate experimental values associated with a signature $\alpha =+\frac{1}{2}$ ($-\frac{1}{2}$) sequence. Symbols with arrows indicate either upper or lower limits established by the lifetime measurements. The dashed (solid) curve represents theoretical predictions from cranked Woods-Saxon calculations for band 6 (7) with signature $\alpha =-\frac{1}{2}$ ($+\frac{1}{2}$), as indicated in the figure.